Free vibration analysis of a rotating beam with nonlinear spring and mass system

Abstract Free, out of plane vibration of a rotating beam with nonlinear spring–mass system has been investigated. The nonlinear constraint is connected to the beam between two points on the beam through a rigid rod. Formulation of the equation of motion is obtained starting from transverse/axial coupling through axial strain. Solution is obtained by applying method of multiple time scale directly to the nonlinear partial differential equations and the boundary conditions. The results of the linear frequencies match well with those obtained in open literature. Subsequent nonlinear study indicates that there is a pronounced effect of spring and its mass. The influence of rigid rod location on frequencies is also investigated on nonlinear frequencies of rotating beam.

[1]  A. Nayfeh.  Introduction To Perturbation Techniques , 1981 .

[2]  John Dugundji,et al.  Experiments and analysis for composite blades under large deflections. II - Dynamic behavior , 1990 .

[3]  Ali H. Nayfeh,et al.  A numerical-perturbation method for the nonlinear analysis of structural vibrations , 1974 .

[4]  A. Nayfeh,et al.  Nonlinear vibrations of a beam-spring-mass system , 1994 .

[5]  Comandur Venkatesan,et al.  Elastomeric Damper Model and Limit Cycle Oscillation in Bearingless Helicopter Rotor Blade , 2000 .

[6]  G. Pohit,et al.  Large Amplitude Free Vibration Analysis of a Rotating Beam with Non-linear Spring and Mass System , 2005 .

[7]  Earl H. Dowell,et al.  Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades , 1974 .

[8]  Edward C. Smith,et al.  EFFICIENT MODELING OF ELASTOMERIC MATERIALS USING FRACTIONAL DERIVATIVES AND PLASTIC YIELDING , 2001 .

[9]  P. Friedmann,et al.  The Nonlinear Behavior of Elastic Slender Straight Beams Undergoing Small Strains and Moderate Rotations , 1979 .

[10]  Christophe Pierre,et al.  Modal Reduction of a Nonlinear Rotating Beam Through Nonlinear Normal Modes , 2002 .

[11]  Ali H. Nayfeh,et al.  Nonlinear Normal Modes of a Cantilever Beam , 1995 .

[12]  G. L. Anderson,et al.  On the extensional and flexural vibrations of rotating bars , 1975 .

[13]  J. L. Potter.  Improving Reliability and Eliminating Maintenance with Elastomeric Dampers for Rotor Systems , 1973 .

[14]  Comandur Venkatesan,et al.  Influence of nonlinear elastomer on isolated lag dynamics and rotor/fuselage aeromechanical stability , 2000 .

[15]  George A. Lesieutre,et al.  Rotorcraft blade lag damping using highly distributed tuned vibration absorbers , 1998 .

[16]  A. K. Mallik,et al.  FREE OUT-OF-PLANE VIBRATIONS OF A ROTATING BEAM WITH NON-LINEAR ELASTOMERIC CONSTRAINTS , 1999 .

[17]  O. Bauchau.  A Beam Theory for Anisotropic Materials , 1985 .

[18]  Ali H. Nayfeh,et al.  Nonlinear Normal Modes of a Continuous System With Quadratic Nonlinearities , 1995 .